Bit interleaver for low-density parity check codeword having length of 64800 and code rate of 3/15 and 16-symbol mapping, and bit interleaving method using same

ABSTRACT

A bit interleaver, a bit-interleaved coded modulation (BICM) device and a bit interleaving method are disclosed herein. The bit interleaver includes a first memory, a processor, and a second memory. The first memory stores a low-density parity check (LDPC) codeword having a length of 64800 and a code rate of 3/15. The processor generates an interleaved codeword by interleaving the LDPC codeword on a bit group basis. The size of the bit group corresponds to a parallel factor of the LDPC codeword. The second memory provides the interleaved codeword to a modulator for 16-symbol mapping.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/626,238, filed Feb. 19, 2015, which claims the benefit of KoreanPatent Application Nos. 10-2014-0019879, 10-2014-0023603 and10-2015-0021506, filed Feb. 20, 2014, Feb. 27, 2014, and Feb. 12, 2015,respectively, which are hereby incorporated by reference herein in theirentirety.

BACKGROUND

1. Technical Field

The present disclosure relates generally to an interleaver and, moreparticularly, to a bit interleaver that is capable of distributing bursterrors occurring in a digital broadcast channel.

2. Description of the Related Art

Bit-Interleaved Coded Modulation (BICM) is bandwidth-efficienttransmission technology, and is implemented in such a manner that anerror-correction coder, a bit-by-bit interleaver and a high-ordermodulator are combined with one another.

BICM can provide excellent performance using a simple structure becauseit uses a low-density parity check (LDPC) coder or a Turbo coder as theerror-correction coder. Furthermore, BICM can provide high-levelflexibility because it can select modulation order and the length andcode rate of an error correction code in various forms. Due to theseadvantages, BICM has been used in broadcasting standards, such as DVB-T2and DVB-NGH, and has a strong possibility of being used in othernext-generation broadcasting systems.

However, in spite of those advantages, BICM suffers from the rapiddegradation of performance unless burst errors occurring in a channelare appropriately distributed via the bit-by-bit interleaver.Accordingly, the bit-by-bit interleaver used in BICM should be designedto be optimized for the modulation order or the length and code rate ofthe error correction code.

SUMMARY

At least one embodiment of the present invention is directed to theprovision of an intra-BICM bit interleaver that can effectivelydistribute burst errors occurring in a broadcasting system channel.

At least one embodiment of the present invention is directed to theprovision of a bit interleaver that is optimized for an LDPC coderhaving a length of 64800 and a code rate of 3/15 and a modulatorperforming 16-symbol mapping and, thus, can be applied tonext-generation broadcasting systems, such as ATSC 3.0.

In accordance with an aspect of the present invention, there is provideda bit interleaver, including a first memory configured to store alow-density parity check (LDPC) codeword having a length of 64800 and acode rate of 3/15; a processor configured to generate an interleavedcodeword by interleaving the LDPC codeword on a bit group basis, thesize of the bit group corresponding to a parallel factor of the LDPCcodeword; and a second memory configured to provide the interleavedcodeword to a modulator for 16-symbol mapping.

The 16-symbol mapping may be NUC (Non-Uniform Constellation) symbolmapping corresponding to 16 constellations (symbols).

The parallel factor may be 360, and each of the bit groups may include360 bits.

The LDPC codeword may be represented by (u₀, u₁, . . . , u_(N) _(ldpc)⁻¹) (where N_(ldpc) is 64800), and may be divided into 180 bit groupseach including 360 bits, as in the following equation:

X _(j) ={u _(k)|360×j≦k<360×(j+1), 0≦k<N _(ldpc)} for 0≦j<N _(group)

where X_(j) is an j-th bit group, N_(ldpc) is 64800, and N_(group) is180.

The interleaving may be performed using the following equation usingpermutation order:

Y _(j) =X _(π(j)) 0≦j≦N _(group)

where X_(j) is the j-th bit group, Y_(j) is an interleaved j-th bitgroup, and π(j) is a permutation order for bit group-based interleaving(bit group-unit interleaving).

The permutation order may correspond to an interleaving sequencerepresented by the following equation:

interleaving sequence={52 92 175 26 45 81 117 74 119 147 120 135 144 873 51 20 170 143 125 15 39 5 174 79 16 176 44 19 69 11 111 121 37 160 8850 76 129 138 157 86 113 164 142 98 9 93 166 78 73 167 168 40 131 27 89156 177 171 116 152 0 127 36 8 153 59 75 13 105 55 122 132 172 2 58 126162 30 77 158 17 96 100 42 63 134 154 6 90 128 83 60 146 124 178 99 123108 133 159 151 145 61 53 68 31 41 94 35 21 49 82 80 4 155 7 57 95 62 5665 140 163 148 23 161 169 47 67 139 72 43 110 46 150 109 115 32 14 17985 165 112 25 64 173 10 102 114 71 66 84 24 141 29 104 107 54 12 91 1118 136 18 101 149 130 103 106 38 70 48 28 137 97 34 22 33}

In accordance with another aspect of the present invention, there isprovided a bit interleaving method, including storing an LDPC codewordhaving a length of 64800 and a code rate of 3/15; generating aninterleaved codeword by interleaving the LDPC codeword on a bit groupbasis corresponding to the parallel factor of the LDPC codeword; andoutputting the interleaved codeword to a modulator for 16-symbolmapping.

In accordance with still another aspect of the present invention, thereis provided a BICM device, including an error-correction coderconfigured to output an LDPC codeword having a length of 64800 and acode rate of 3/15; a bit interleaver configured to interleave the LDPCcodeword on a bit group basis corresponding to the parallel factor ofthe LDPC codeword and output the interleaved codeword; and a modulatorconfigured to perform 16-symbol mapping on the interleaved codeword.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features and advantages of the presentinvention will be more clearly understood from the following detaileddescription taken in conjunction with the accompanying drawings, inwhich:

FIG. 1 is a block diagram illustrating a broadcast signal transmissionand reception system according to an embodiment of the presentinvention;

FIG. 2 is an operation flowchart illustrating a broadcast signaltransmission and reception method according to an embodiment of thepresent invention;

FIG. 3 is a diagram illustrating the structure of a parity check matrix(PCM) corresponding to an LDPC code to according to an embodiment of thepresent invention;

FIG. 4 is a diagram illustrating the bit groups of an LDPC codewordhaving a length of 64800;

FIG. 5 is a diagram illustrating the bit groups of an LDPC codewordhaving a length of 16200;

FIG. 6 is a diagram illustrating interleaving that is performed on a bitgroup basis in accordance with an interleaving sequence;

FIG. 7 is a block diagram illustrating a bit interleaver according to anembodiment of the present invention; and

FIG. 8 is an operation flowchart illustrating a bit interleaving methodaccording to an embodiment of the present invention.

DETAILED DESCRIPTION

Embodiments of the present invention will be described in detail belowwith reference to the accompanying drawings. Repeated descriptions anddescriptions of well-known functions and configurations that have beendeemed to make the gist of the present invention unnecessarily obscurewill be omitted below. The embodiments of the present invention areintended to fully describe the present invention to persons havingordinary knowledge in the art to which the present invention pertains.Accordingly, the shapes, sizes, etc. of components in the drawings maybe exaggerated to make the description obvious.

Embodiments of the present invention will be described in detail belowwith reference to the accompanying drawings.

FIG. 1 is a block diagram illustrating a broadcast signal transmissionand reception system according to an embodiment of the presentinvention.

Referring to FIG. 1, it can be seen that a BICM device 10 and a BICMreception device 30 communicate with each other over a wireless channel20.

The BICM device 10 generates an n-bit codeword by encoding k informationbits 11 using an error-correction coder 13. In this case, theerror-correction coder 13 may be an LDPC coder or a Turbo coder.

The codeword is interleaved by a bit interleaver 14, and thus theinterleaved codeword is generated.

In this case, the interleaving may be performed on a bit group basis (bya unit of a bit group). In this case, the error-correction coder 13 maybe an LDPC coder having a length of 64800 and a code rate of 3/15. Acodeword having a length of 64800 may be divided into a total of 180 bitgroups. Each of the bit groups may include 360 bits, i.e., the parallelfactor of an LDPC codeword.

In this case, the interleaving may be performed on a bit group basis (bya unit of a bit group) in accordance with an interleaving sequence,which will be described later.

In this case, the bit interleaver 14 prevents the performance of errorcorrection code from being degraded by effectively distributing bursterrors occurring in a channel. In this case, the bit interleaver 14 maybe separately designed in accordance with the length and code rate ofthe error correction code and the modulation order.

The interleaved codeword is modulated by a modulator 15, and is thentransmitted via an antenna 17.

In this case, the modulator 15 may be based on a concept includingsymbol mapper (symbol mapping device). In this case, the modulator 15may be a symbol mapping device performing 16-symbol mapping which mapscodes onto 16 constellations (symbols).

In this case, the modulator 15 may be a uniform modulator, such as aquadrature amplitude modulation (QAM) modulator, or a non-uniformmodulator.

The modulator 15 may be a symbol mapping device performing NUC(Non-Uniform Constellation) symbol mapping which uses 16 constellations(symbols).

The signal transmitted via the wireless channel 20 is received via theantenna 31 of the BICM reception device 30, and, in the BICM receptiondevice 30, is subjected to a process reverse to the process in the BICMdevice 10. That is, the received data is demodulated by a demodulator33, is deinterleaved by a bit deinterleaver 34, and is then decoded byan error correction decoder 35, thereby finally restoring theinformation bits.

It will be apparent to those skilled in the art that the above-describedtransmission and reception processes have been described within aminimum range required for a description of the features of the presentinvention and various processes required for data transmission may beadded.

FIG. 2 is an operation flowchart illustrating a broadcast signaltransmission and reception method according to an embodiment of thepresent invention.

Referring to FIG. 2, in the broadcast signal transmission and receptionmethod according to this embodiment of the present invention, input bits(information bits) are subjected to error-correction coding at stepS210.

That is, at step S210, an n-bit codeword is generated by encoding kinformation bits using the error-correction coder.

In this case, step S210 may be performed as in an LDPC encoding method,which will be described later.

Furthermore, in the broadcast signal transmission and reception method,an interleaved codeword is generated by interleaving the n-bit codewordon a bit group basis at step S220.

In this case, the n-bit codeword may be an LDPC codeword having a lengthof 64800 and a code rate of 3/15. The codeword having a length of 64800may be divided into a total of 180 bit groups. Each of the bit groupsmay include 360 bits corresponding to the parallel factors of an LDPCcodeword.

In this case, the interleaving may be performed on a bit group basis (bya unit of a bit group) in accordance with an interleaving sequence,which will be described later.

Furthermore, in the broadcast signal transmission and reception method,the encoded data is modulated at step S230.

That is, at step S230, the interleaved codeword is modulated using themodulator.

In this case, the modulator may be based on a concept including symbolmapper (symbol mapping device). In this case, the modulator may be asymbol mapping device performing 16-symbol mapping which maps codes onto16 constellations (symbols).

In this case, the modulator may be a uniform modulator, such as a QAMmodulator, or a non-uniform modulator.

The modulator may be a symbol mapping device performing NUC (Non-UniformConstellation) symbol mapping which uses 16 constellations (symbols).

Furthermore, in the broadcast signal transmission and reception method,the modulated data is transmitted at step S240.

That is, at step S240, the modulated codeword is transmitted over thewireless channel via the antenna.

Furthermore, in the broadcast signal transmission and reception method,the received data is demodulated at step S250.

That is, at step S250, the signal transmitted over the wireless channelis received via the antenna of the receiver, and the received data isdemodulated using the demodulator.

Furthermore, in the broadcast signal transmission and reception method,the demodulated data is deinterleaved at step S260. In this case, thedeinterleaving of step S260 may be reverse to the operation of stepS220.

Furthermore, in the broadcast signal transmission and reception method,the deinterleaved codeword is subjected to error correction decoding atstep S270.

That is, at step S270, the information bits are finally restored byperforming error correction decoding using the error correction decoderof the receiver.

In this case, step S270 corresponds to a process reverse to that of anLDPC encoding method, which will be described later.

An LDPC code is known as a code very close to the Shannon limit for anadditive white Gaussian noise (AWGN) channel, and has the advantages ofasymptotically excellent performance and parallelizable decodingcompared to a turbo code.

Generally, an LDPC code is defined by a low-density parity check matrix(PCM) that is randomly generated. However, a randomly generated LDPCcode requires a large amount of memory to store a PCM, and requires alot of time to access memory. In order to overcome these problems, aquasi-cyclic LDPC (QC-LDPC) code has been proposed. A QC-LDPC code thatis composed of a zero matrix or a circulant permutation matrix (CPM) isdefined by a PCM that is expressed by the following Equation 1:

$\begin{matrix}{{H = \begin{bmatrix}J^{a_{11}} & J^{a_{12}} & \ldots & J^{a_{1n}} \\J^{a_{21}} & J^{a_{22}} & \ldots & J^{a_{2n}} \\\vdots & \vdots & \ddots & \vdots \\J^{a_{m\; 1}} & J^{a_{m\; 2}} & \ldots & J^{a_{mn}}\end{bmatrix}},{{{for}\mspace{14mu} a_{ij}} \in \left\{ {0,1,\ldots \mspace{14mu},{L - 1},\infty} \right\}}} & (1)\end{matrix}$

In this equation, J is a CPM having a size of L×L, and is given as thefollowing Equation 2. In the following description, L may be 360.

$\begin{matrix}{J_{L \times L} = \begin{bmatrix}0 & 1 & 0 & \ldots & 0 \\0 & 0 & 1 & \ldots & 0 \\\vdots & \vdots & \vdots & \ddots & \vdots \\0 & 0 & 0 & \ldots & 1 \\1 & 0 & 0 & \ldots & 0\end{bmatrix}} & (2)\end{matrix}$

Furthermore, J^(i) is obtained by shifting an L×L identity matrix I (J⁰)to the right i (0≦i<L) times, and J^(∞) is an L×L zero matrix.Accordingly, in the case of a QC-LDPC code, it is sufficient if onlyindex exponent i is stored in order to store J^(i), and thus the amountof memory required to store a PCM is considerably reduced.

FIG. 3 is a diagram illustrating the structure of a PCM corresponding toan LDPC code to according to an embodiment of the present invention.

Referring to FIG. 3, the sizes of matrices A and C are g×K and(N−K−g)×(K+g), respectively, and are composed of an L×L zero matrix anda CPM, respectively. Furthermore, matrix Z is a zero matrix having asize of g×(N−K−g), matrix D is an identity matrix having a size of(N−K−g)×(N−K−g), and matrix B is a dual diagonal matrix having a size ofg×g. In this case, the matrix B may be a matrix in which all elementsexcept elements along a diagonal line and neighboring elements below thediagonal line are 0, and may be defined as the following Equation 3:

$\begin{matrix}{B_{g \times g} = \begin{bmatrix}I_{L \times L} & 0 & 0 & \ldots & 0 & 0 & 0 \\I_{L \times L} & I_{L \times L} & 0 & \ldots & 0 & 0 & 0 \\0 & I_{L \times L} & I_{L \times L} & \vdots & 0 & 0 & 0 \\\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots \\0 & 0 & 0 & \ldots & I_{L \times L} & I_{L \times L} & 0 \\0 & 0 & 0 & \ldots & 0 & I_{L \times L} & I_{L \times L}\end{bmatrix}} & (3)\end{matrix}$

where I_(L×L) is an identity matrix having a size of L×L.

That is, the matrix B may be a bit-wise dual diagonal matrix, or may bea block-wise dual diagonal matrix having identity matrices as itsblocks, as indicated by Equation 3. The bit-wise dual diagonal matrix isdisclosed in detail in Korean Patent Application Publication No.2007-0058438, etc.

In particular, it will be apparent to those skilled in the art that whenthe matrix B is a bit-wise dual diagonal matrix, it is possible toperform conversion into a Quasi-cyclic form by applying row or columnpermutation to a PCM including the matrix B and having a structureillustrated in FIG. 3.

In this case, N is the length of a codeword, and K is the length ofinformation.

The present invention proposes a newly designed QC-LDPC code in whichthe code rate thereof is 3/15 and the length of a codeword is 64800, asillustrated in the following Table 1. That is, the present inventionproposes an LDPC code that is designed to receive information having alength of 12960 and generate an LDPC codeword having a length of 64800.

Table 1 illustrates the sizes of the matrices A, B, C, D and Z of theQC-LDPC code according to the present invention:

TABLE 1 Sizes Code rate Length A B C D Z 3/15 64800 1800 × 12960 1800 ×1800 50040 × 14760 50040 × 50040 1800 × 50040

The newly designed LDPC code may be represented in the form of asequence (progression), an equivalent relationship is establishedbetween the sequence and matrix (parity bit check matrix), and thesequence may be represented, as follows:

Sequence Table 1st row: 920 963 1307 2648 6529 17455 18883 19848 1990924149 24249 38395 41589 48032 50313 2nd row: 297 736 744 5951 8438 988115522 16462 23036 25071 34915 41193 42975 43412 49612 3rd row: 10 223879 4662 6400 8691 14561 16626 17408 22810 31795 32580 43639 45223 475114th row: 629 842 1666 3150 7596 9465 12327 18649 19052 19279 29743 3019740106 48371 51155 5th row: 857 953 1116 8725 8726 10508 17112 2100730649 32113 36962 39254 46636 49599 50099 6th row: 700 894 1128 55276216 15123 21510 24584 29026 31416 37158 38460 42511 46932 51832 7throw: 430 592 1521 3018 10430 18090 18092 18388 20017 34383 35006 3825541700 42158 45211 8th row: 91 1485 1733 11624 12969 17531 21324 2365727148 27509 28753 35093 43352 48104 51648 9th row: 18 34 117 6739 867911018 12163 16733 24113 25906 30605 32700 36465 40799 43359 10th row:481 1545 1644 4216 4606 6015 6609 14659 16966 18056 19137 26670 2800130668 49061 11st row: 174 1208 1387 10580 11507 13751 16344 22735 2355926492 27672 33399 44787 44842 45992 12nd row: 1151 1185 1472 6727 1070114755 15688 17441 21281 23692 23994 31366 35854 37301 43148 13rd row:200 799 1583 3451 5880 7604 8194 13428 16109 18584 20463 22373 3197747073 50087 14th row: 346 843 1352 13409 17376 18233 19119 19382 2057824183 32052 32912 43204 48539 49893 15th row: 76 457 1169 13516 1452014638 22391 25294 31067 31325 36711 44072 44854 49274 51624 16th row:759 798 1420 6661 12101 12573 13796 15510 18384 26649 30875 36856 3899443634 49281 17th row: 551 797 1000 3999 10040 11246 15793 23298 2382238480 39209 45334 46603 46625 47633 18th row: 441 875 1554 5336 2594828842 30329 31503 39203 39673 46250 47021 48555 49229 51421 19th row:963 1470 1642 3180 3943 6513 9125 15641 17083 18876 28499 32764 4242043922 45762 20th row: 293 324 867 8803 10582 17926 19830 22497 2484830034 34659 37721 41523 42534 47806 21st row: 687 975 1356 2721 30023874 4119 12336 17119 21251 22482 22833 24681 26225 48514 22nd row: 549951 1268 9144 11710 12623 18949 19362 22769 32603 34559 34683 3633847140 51069 23rd row: 52 890 1669 3905 5670 14712 18314 22297 3032833389 35447 35512 35516 40587 41918 24th row: 656 1063 1694 3338 37934513 6009 7441 13393 20920 26501 27576 29623 31261 42093 25th row: 4251018 1086 9226 10024 17552 24714 24877 25853 28918 30945 31205 3310342564 47214 26th row: 32 1145 1438 4916 4945 14830 17505 19919 2411828506 30173 31754 34230 48608 50291 27th row: 559 1216 1272 2856 87039371 9708 16180 19127 24337 26390 36649 41105 42988 44096 28th row: 362658 1191 7769 8998 14068 15921 18471 18780 31995 32798 32864 37293 3946844308 29th row: 1136 1389 1785 8800 12541 14723 15210 15859 26569 3012731357 32898 38760 50523 51715 30th row: 44 80 1368 2010 2228 6614 67679275 25237 30208 39537 42041 49906 50701 51199 31st row: 1522 1536 17653914 5350 10869 12278 12886 16379 22743 23987 26306 30966 33854 4135632nd row: 212 648 709 3443 7007 7545 12484 13358 17008 20433 25862 3194539207 39752 40313 33rd row: 789 1062 1431 12280 17415 18098 23729 3727838454 38763 41039 44600 50700 51139 51696 34th row: 825 1298 1391 488212738 17569 19177 19896 27401 37041 39181 39199 41832 43636 45775 35throw: 992 1053 1485 3806 16929 18596 22017 23435 23932 30211 30390 3446937213 46220 49646 36th row: 771 850 1039 5180 7653 13547 17980 2336525318 34374 36115 38753 42993 49696 51031 37th row: 7383 14780 1595918921 22579 28612 32038 36727 40851 41947 42707 50480 38th row: 87339464 13148 13899 19396 22933 23039 25047 29938 33588 33796 48930 39throw: 2493 12555 16706 23905 35400 36330 37065 38866 40305 43807 4391750621 40th row: 6437 11927 14542 16617 17317 17755 18832 24772 2927331136 36925 46663 41st row: 2191 3431 6288 6430 9908 13069 23014 2482229818 39914 46010 47246

An LDPC code that is represented in the form of a sequence is beingwidely used in the DVB standard.

According to an embodiment of the present invention, an LDPC codepresented in the form of a sequence is encoded, as follows. It isassumed that there is an information block S=(s₀, s₁, . . . , s_(K−1))having an information size K. The LDPC encoder generates a codewordΛ=(λ₀, λ₁, λ₂, . . . , λ_(N−1)) having a size of N=K+M₁+M₂ using theinformation block S having a size K. In this case, M₁=g, and M₂=N−K−g.Furthermore, M₁ is the size of parity bits corresponding to the dualdiagonal matrix B, and M₂ is the size of parity bits corresponding tothe identity matrix D. The encoding process is performed, as follows:

Initialization:

λ_(i) =s _(i) for i=0, 1, . . . , K−1

p _(j)=0 for j=0, 1, . . . , M ₁ +M ₂−1  (4)

First information bit λ₀ is accumulated at parity bit addressesspecified in the 1st row of the sequence of the Sequence Table. Forexample, in an LDPC code having a length of 64800 and a code rate of3/15, an accumulation process is as follows:

-   p₉₂₅=p₉₂₅⊕λp₉₆₈=p₉₆₈⊕λp₁₃₁₂=p₁₃₁₂⊕λp₂₇₈₇=p₂₇₈₇⊕λp₆₆₆₈=p₆₆₆₈⊕λ-   p₁₇₅₉₄=p₁₇₅₉₄⊕λp₁₉₀₂₂=p₁₉₀₂₂⊕λp₁₉₉₈₇=p₁₉₉₈₇⊕λp₂₀₀₄₈=p₂₀₀₄₈⊕λp₂₄₂₈₈=p₂₄₂₈₈⊕λ-   p₂₄₃₈₈=p₂₄₃₈₈⊕λp₃₈₅₃₄=p₃₈₅₃₄⊕λp₄₁₇₂₈=p₄₁₇₂₈⊕λp₄₈₁₇₁=p₄₈₁₇₁⊕λp₅₀₄₅₂=p₅₀₄₅₂⊕λ    where the addition ⊕ occurs in GF(2).

The subsequent L−1 information bits, that is, λ_(m), m=1, 2, . . . ,L−1, are accumulated at parity bit addresses that are calculated by thefollowing Equation 5:

(x+m×Q ₁) mod M ₁ if x<M ₁

M ₁+{(x−M ₁ +m×Q ₂) mod M ₂} if x≧M ₁  (5)

where x denotes the addresses of parity bits corresponding to the firstinformation bit λ₀, that is, the addresses of the parity bits specifiedin the first row of the sequence of the Sequence Table, Q₁=M₁/L,Q₂=M₂/L, and L=360. Furthermore, Q₁ and Q₂ are defined in the followingTable 2. For example, for an LDPC code having a length of 64800 and acode rate of 3/15, M₁=1800, Q₁=5, M₂=50040, Q₂=139 and L=360, and thefollowing operations are performed on the second bit λ₁ using Equation5:

-   p₉₂₅=p₉₂₅⊕λp₉₆₈=p₉₆₈⊕λp₁₃₁₂=p₁₃₁₂⊕λp₂₇₈₇=p₂₇₈₇⊕λp₆₆₆₈=p₆₆₆₈⊕λ-   p₁₇₅₉₄=p₁₇₅₉₄⊕λp₁₉₀₂₂=p₁₉₀₂₂⊕λp₁₉₉₈₇=p₁₉₉₈₇⊕λp₂₀₀₄₈=p₂₀₀₄₈⊕λp₂₄₂₈₈=p₂₄₂₈₈⊕λ-   p₂₄₃₈₈=p₂₄₃₈₈⊕λp₃₈₅₃₄=p₃₈₅₃₄⊕λp₄₁₇₂₈=p₄₁₇₂₈⊕λp₄₈₁₇₁=p₄₈₁₇₁⊕λp₅₀₄₅₂=p₅₀₄₅₂⊕λ

Table 2 illustrates the sizes of M₁, Q₁, M₂ and Q₂ of the designedQC-LDPC code:

TABLE 2 Sizes Code rate Length M₁ M₂ Q₁ Q₂ 3/15 64800 1800 50040 5 139

The addresses of parity bit accumulators for new 360 information bitsfrom λ_(L) to λ_(2L-1) are calculated and accumulated from Equation 5using the second row of the sequence.

In a similar manner, for all groups composed of new L information bits,the addresses of parity bit accumulators are calculated and accumulatedfrom Equation 5 using new rows of the sequence.

After all the information bits from λ₀ to λ_(K−1) have been exhausted,the operations of the following Equation 6 are sequentially performedfrom i=1:

p _(i) =p _(i) ⊕p _(i-1) for i=0, 1, . . . , M ₁−1  (6)

Thereafter, when a parity interleaving operation, such as that of thefollowing Equation 7, is performed, parity bits corresponding to thedual diagonal matrix B are generated:

λ_(K+L·t+s) =p _(Q) ₁ _(·s+t) for 0≦s<L, 0≦t<Q ₁  (7)

When the parity bits corresponding to the dual diagonal matrix B havebeen generated using K information bits λ₀, λ₁, . . . , λ_(K−1), paritybits corresponding to the identity matrix D are generated using the M₁generated parity bits λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹.

For all groups composed of L information bits from λ_(K) to λ_(K+M) ₁⁻¹, the addresses of parity bit accumulators are calculated using thenew rows (starting with a row immediately subsequent to the last rowused when the parity bits corresponding to the dual diagonal matrix Bhave been generated) of the sequence and Equation 5, and relatedoperations are performed.

When a parity interleaving operation, such as that of the followingEquation 8, is performed after all the information bits from λ_(K) toλ_(K+M) ₁ ⁻¹ have been exhausted, parity bits corresponding to theidentity matrix D are generated:

λ_(K+M) ₁ _(+L·t+s) =p _(M) ₁ _(+Q) ₂ _(·s+t) for 0≦s<L, 0≦t<Q ₂  (8)

FIG. 4 is a diagram illustrating the bit groups of an LDPC codewordhaving a length of 64800.

Referring to FIG. 4, it can be seen that an LDPC codeword having alength of 64800 is divided into 180 bit groups (a 0th group to a 179thgroup).

In this case, 360 may be the parallel factor (PF) of the LDPC codeword.That is, since the PF is 360, the LDPC codeword having a length of 64800is divided into 180 bit groups, as illustrated in FIG. 4, and each ofthe bit groups includes 360 bits.

FIG. 5 is a diagram illustrating the bit groups of an LDPC codewordhaving a length of 16200.

Referring to FIG. 5, it can be seen that an LDPC codeword having alength of 16200 is divided into 45 bit groups (a 0th group to a 44thgroup).

In this case, 360 may be the parallel factor (PF) of the LDPC codeword.That is, since the PF is 360, the LDPC codeword having a length of 16200is divided into 45 bit groups, as illustrated in FIG. 5, and each of thebit groups includes 360 bits.

FIG. 6 is a diagram illustrating interleaving that is performed on a bitgroup basis in accordance with an interleaving sequence.

Referring to FIG. 6, it can be seen that interleaving is performed bychanging the order of bit groups by a designed interleaving sequence.

For example, it is assumed that an interleaving sequence for an LDPCcodeword having a length of 16200 is as follows:

interleaving sequence={24 34 15 11 2 28 17 25 5 38 19 13 6 39 1 14 33 3729 12 42 31 30 32 36 40 26 35 44 4 16 8 20 43 21 7 0 18 23 3 10 41 9 2722}

Then, the order of the bit groups of the LDPC codeword illustrated inFIG. 4 is changed into that illustrated in FIG. 6 by the interleavingsequence.

That is, it can be seen that each of the LDPC codeword 610 and theinterleaved codeword 620 includes 45 bit groups, and it can be also seenthat, by the interleaving sequence, the 24th bit group of the LDPCcodeword 610 is changed into the 0th bit group of the interleaved LDPCcodeword 620, the 34th bit group of the LDPC codeword 610 is changedinto the 1st bit group of the interleaved LDPC codeword 620, the 15thbit group of the LDPC codeword 610 is changed into the 2nd bit group ofthe interleaved LDPC codeword 620, and the 11st bit group of the LDPCcodeword 610 is changed into the 3rd bit group of the interleaved LDPCcodeword 620, and the 2nd bit group of the LDPC codeword 610 is changedinto the 4th bit group of the interleaved LDPC codeword 620.

An LDPC codeword (u₀, u₁, . . . , u_(N) _(ldpc) ⁻¹) having a length ofN_(ldpc) is divided into N_(group)=N_(ldpc)/360 bit groups, as inEquation 9 below:

X _(j) ={u _(k)|360×j≦k<360×(j+1), 0≦k<N _(ldpc)} for 0≦j<N_(group)  (9)

where X_(j) is an j-th bit group, and each X_(j) is composed of 360bits.

The LDPC codeword divided into the bit groups is interleaved, as inEquation 10 below:

Y _(j) =X _(π(j)) 0≦j≦N _(group)  (10)

where Y_(j) is an interleaved j-th bit group, and π(j) is a permutationorder for bit group-based interleaving (bit group-unit interleaving).The permutation order corresponds to the interleaving sequence ofEquation 11 below:

interleaving sequence={52 92 175 26 45 81 117 74 119 147 120 135 144 873 51 20 170 143 125 15 39 5 174 79 16 176 44 19 69 11 111 121 37 160 8850 76 129 138 157 86 113 164 142 98 9 93 166 78 73 167 168 40 131 27 89156 177 171 116 152 0 127 36 8 153 59 75 13 105 55 122 132 172 2 58 126162 30 77 158 17 96 100 42 63 134 154 6 90 128 83 60 146 124 178 99 123108 133 159 151 145 61 53 68 31 41 94 35 21 49 82 80 4 155 7 57 95 62 5665 140 163 148 23 161 169 47 67 139 72 43 110 46 150 109 115 32 14 17985 165 112 25 64 173 10 102 114 71 66 84 24 141 29 104 107 54 12 91 1118 136 18 101 149 130 103 106 38 70 48 28 137 97 34 22 33}  (11)

That is, when each of the codeword and the interleaved codeword includes180 bit groups ranging from a 0th bit group to a 179th bit group, theinterleaving sequence of Equation 11 means that the 52nd bit group ofthe codeword becomes the 0th bit group of the interleaved codeword, the92nd bit group of the codeword becomes the 1st bit group of theinterleaved codeword, the 175th bit group of the codeword becomes the2nd bit group of the interleaved codeword, the 26th bit group of thecodeword becomes the 3rd bit group of the interleaved codeword, . . . ,the 22th bit group of the codeword becomes the 178th bit group of theinterleaved codeword, and the 33th bit group of the codeword becomes the179th bit group of the interleaved codeword.

In particular, the interleaving sequence of Equation 11 has beenoptimized for a case where 16-symbol mapping (NUC symbol mapping) isemployed and an LDPC coder having a length of 64800 and a code rate of3/15 is used.

FIG. 7 is a block diagram illustrating a bit interleaver according to anembodiment of the present invention.

Referring to FIG. 7, the bit interleaver according to the presentembodiment includes memories 710 and 730 and a processor 720.

The memory 710 stores an LDPC codeword having a length of 64800 and acode rate of 3/15.

The processor 720 generates an interleaved codeword by interleaving theLDPC codeword on a bit group basis corresponding to the parallel factorof the LDPC codeword.

In this case, the parallel factor may be 360. In this case, each of thebit groups may include 360 bits.

In this case, the LDPC codeword may be divided into 180 bit groups, asin Equation 9.

In this case, the interleaving may be performed using Equation 10 usingpermutation order.

In this case, the permutation order may correspond to the interleavingsequence represented by Equation 11.

The memory 730 provides the interleaved codeword to a modulator for16-symbol mapping.

In this case, the modulator may be a symbol mapping device performingNUC (Non-Uniform Constellation) symbol mapping.

The memories 710 and 730 may correspond to various types of hardware forstoring a set of bits, and may correspond to a data structure, such asan array, a list, a stack, a queue or the like.

In this case, the memories 710 and 730 may not be physically separatedevices, but may correspond to different addresses of a physicallysingle device. That is, the memories 710 and 730 are not physicallydistinguished from each other, but are merely logically distinguishedfrom each other.

The error-correction coder 13 illustrated in FIG. 1 may be implementedin the same structure as in FIG. 7.

That is, the error-correction coder may include memories and aprocessor. In this case, the first memory is a memory that stores anLDPC codeword having a length of 64800 and a code rate of 3/15, and asecond memory is a memory that is initialized to 0.

The memories may correspond to λ_(i) (i=0, 1, . . . , N−1) andP_(j)(j=0, 1, . . . , M₁+M₂−1), respectively.

The processor may generate an LDPC codeword corresponding to informationbits by performing accumulation with respect to the memory using asequence corresponding to a parity check matrix (PCM).

In this case, the accumulation may be performed at parity bit addressesthat are updated using the sequence of the above Sequence Table.

In this case, the LDPC codeword may include a systematic part λ₀, λ₁, .. . , λ_(K−1) corresponding to the information bits and having a lengthof 12960 (=K), a first parity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹corresponding to a dual diagonal matrix included in the PCM and having alength of 1800 (=M₁=g), and a second parity part λ_(K+M) ₁ , λ_(K+M) ₁₊₁, . . . , λ_(K+M) ₁ _(+M) ₂ ⁻¹ corresponding to an identity matrixincluded in the PCM and having a length of 50040 (=M₂).

In this case, the sequence may have a number of rows equal to the sum(12960/360+1800/360=41) of a value obtained by dividing the length ofthe systematic part, i.e., 12960, by a CPM size L corresponding to thePCM, i.e., 360, and a value obtained by dividing the length M₁ of thefirst parity part, i.e., 1800, by 360.

As described above, the sequence may be represented by the aboveSequence Table.

In this case, the second memory may have a size corresponding to the sumM₁+M₂ of the length M₁ of the first parity part and the length M₂ of thesecond parity part.

In this case, the parity bit addresses may be updated based on theresults of comparing each x of the previous parity bit addresses,specified in respective rows of the sequence, with the length M₁ of thefirst parity part.

That is, the parity bit addresses may be updated using Equation 5. Inthis case, x may be the previous parity bit addresses, m may be aninformation bit index that is an integer larger than 0 and smaller thanL, L may be the CPM size of the PCM, Q₁ may be M₁/L, M₁ may be the sizeof the first parity part, Q₂ may be M₂/L, and M₂ may be the size of thesecond parity part.

In this case, it may be possible to perform the accumulation whilerepeatedly changing the rows of the sequence by the CPM size L (=360) ofthe PCM, as described above.

In this case, the first parity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹may be generated by performing parity interleaving using the firstmemory and the second memory, as described in conjunction with Equation7.

In this case, the second parity part λ_(K+M) ₁ , λ_(K+M) ₁ ₊₁, . . . ,λ_(K+M) ₁ _(+M) ₂ ⁻¹ may be generated by performing parity interleavingusing the first memory and the second memory after generating the firstparity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹ and then performing theaccumulation using the first parity part λ_(K), λ_(K+1), . . . , λ_(K+M)₁ ⁻¹ and the sequence, as described in conjunction with Equation 8.

FIG. 8 is an operation flowchart illustrating a bit interleaving methodaccording to an embodiment of the present invention.

Referring to FIG. 8, in the bit interleaving method according to thepresent embodiment, an LDPC codeword having a length of 64800 and a coderate of 3/15 is stored at step S810.

In this case, the LDPC codeword may be represented by (u₀, u₁, . . . ,u_(N) _(ldpc) ⁻¹) (where N_(ldpc) is 64800), and may be divided into 180bit groups each composed of 360 bits, as in Equation 9.

Furthermore, in the bit interleaving method according to the presentembodiment, an interleaved codeword is generated by interleaving theLDPC codeword on a bit group basis at step S820.

In this case, the size of the bit group may correspond to the parallelfactor of the LDPC codeword.

In this case, the interleaving may be performed using Equation 10 usingpermutation order.

In this case, the permutation order may correspond to the interleavingsequence represented by Equation 11.

In this case, the parallel factor may be 360, and each of the bit groupsmay include 360 bits.

In this case, the LDPC codeword may be divided into 180 bit groups, asin Equation 9.

Moreover, in the bit interleaving method according to the presentembodiment, the interleaved codeword is output to a modulator for16-symbol mapping at step 830.

In accordance with at least one embodiment of the present invention,there is provided an intra-BICM bit interleaver that can effectivelydistribute burst errors occurring in a broadcasting system channel.

In accordance with at least one embodiment of the present invention,there is provided a bit interleaver that is optimized for an LDPC coderhaving a length of 64800 and a code rate of 3/15 and a modulatorperforming 16-symbol mapping and, thus, can be applied tonext-generation broadcasting systems, such as ATSC 3.0.

Although the specific embodiments of the present invention have beendisclosed for illustrative purposes, those skilled in the art willappreciate that various modifications, additions and substitutions arepossible without departing from the scope and spirit of the invention asdisclosed in the accompanying claims.

What is claimed is:
 1. A bit interleaving method, comprising: storing alow-density parity check (LDPC) codeword having a length of 64800 and acode rate of 3/15; generating an interleaved codeword by interleavingthe LDPC codeword on a bit group basis, the size of the bit groupcorresponding to a parallel factor of the LDPC codeword; and storing theinterleaved codeword corresponding to 16-symbol mapping.
 2. The bitinterleaving method of claim 1, wherein the 16-symbol mapping is aNon-Uniform Constellation (NUC) symbol mapping which corresponds to 16constellations.
 3. The bit interleaving method of claim 2, wherein theparallel factor is 360, and the bit group includes 360 bits.
 4. The bitinterleaving method of claim 3, wherein the LDPC codeword is representedby (u₀, u₁, . . . , u_(N) _(ldpc) ⁻¹) (where N_(ldpc) is 64800), and isdivided into 180 bit groups each including 360 bits, as in the followingequation:X _(j) ={u _(k)|360×j≦k<360×(j+1), 0≦k<N _(ldpc)} for 0≦j<N _(group)where X_(j) is an j-th bit group, N_(ldpc) is 64800, and N_(group) is180.
 5. The bit interleaving method of claim 1, wherein the interleavingis performed using the following equation using permutation order:Y _(j) =X _(π(j)) 0≦j≦N _(group) where X_(π(j)) is the π(j)th bit group,Y_(j) is an interleaved j-th bit group, and π(j) is a permutation orderfor bit group-based interleaving.
 6. The bit interleaving method ofclaim 5, wherein the permutation order corresponds to an interleavingsequence represented by the followinginterleaving sequence={52 92 175 26 45 81 117 74 119 147 120 135 144 873 51 20 170 143 125 15 39 5 174 79 16 176 44 19 69 11 111 121 37 160 8850 76 129 138 157 86 113 164 142 98 9 93 166 78 73 167 168 40 131 27 89156 177 171 116 152 0 127 36 8 153 59 75 13 105 55 122 132 172 2 58 126162 30 77 158 17 96 100 42 63 134 154 6 90 128 83 60 146 124 178 99 123108 133 159 151 145 61 53 68 31 41 94 35 21 49 82 80 4 155 7 57 95 62 5665 140 163 148 23 161 169 47 67 139 72 43 110 46 150 109 115 32 14 17985 165 112 25 64 173 10 102 114 71 66 84 24 141 29 104 107 54 12 91 1118 136 18 101 149 130 103 106 38 70 48 28 137 97 34 22 33}.